A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.
Available: https://arxiv.org/abs/2101.04125
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Numerical simulations of the surface-code ML decoder under single- and two-qubit unitary rotations reveal a ferromagnetic volume-law phase in which classical information is retained yet hard to recover.
A distributed (6.6.6) color code is realized by interconnecting patches via entangled pairs, with simulations showing the concatenated MWPM decoder maintains error threshold under asymmetric seam noise while tensor-network decoder shows slight reduction.
A topical review unifying statistical mechanics, tensor network, and AI approaches to approximate maximum likelihood decoding for quantum error correction codes.
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Non-linear Sigma Model for the Surface Code with Coherent Errors
A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.
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Maximum Likelihood Decoding of Quantum Error Correction Codes
A topical review unifying statistical mechanics, tensor network, and AI approaches to approximate maximum likelihood decoding for quantum error correction codes.